### Abstract

The size of large minimal blocking sets is bounded by the Bruen-Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non-square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non-prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q^{4/3} + 1 or q^{4!3} + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non-prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval (Equation presented).

Original language | English |
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Pages (from-to) | 25-41 |

Number of pages | 17 |

Journal | Journal of Combinatorial Designs |

Volume | 13 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2005 |

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### Keywords

- Blocking sets
- Density results

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Journal of Combinatorial Designs*,

*13*(1), 25-41. https://doi.org/10.1002/jcd.20017